Abstract

A liquid crystal forked vortex lens integrated with Pancharatnam-Berry phase is proposed and demonstrated via a dynamic photo-patterning technique. The forked vortex lens can generate two optical vortices with opposite spin and orbital angular momentum, which are spatially separated to two focal points with one optical vortex focused and the other defocused. It exhibits distinctive helicity-dependency and ultra-high diffraction efficiency up to 95%. The topological charges of generated optical vortices are detected via astigmatic transformation. This work supplies an easy fabrication and low power consumption strategy for generating and separating (de-)focused optical vortices simultaneously.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]

2017 (1)

A. M. Tam, F. Fan, T. Du, W. Hu, W. L. Zhang, C. X. Zhao, X. Q. Wang, K. L. Ching, G. J. Li, H. L. Luo, V. Chigrinov, S. C. Wen, and H. S. Kwok, “Bifocal optical-vortex lens with sorting of the generated nonseparable spin-orbital angular-momentum states,” Phys. Rev. Appl. 7(3), 0304010 (2017).
[Crossref]

2016 (6)

W. Duan, P. Chen, B. Y. Wei, S. J. Ge, X. Liang, W. Hu, and Y. Q. Lu, “Fast-response and high-efficiency optical switch based on dual-frequency liquid crystal polarization grating,” Opt. Mater. Express 6(2), 597–602 (2016).
[Crossref]

A. M. Tam, F. Fan, H. S. Chen, T. Du, V. G. Chigrinov, Y. H. Lin, and H. S. Kwok, “Nanoscopic patterned photo-alignment for electrically switchable liquid crystal Pancharatnam-Berry phase diffractive lens,” J. Soc. Inf. Disp. 47, 599–601 (2016).

J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4(5), B14–B28 (2016).
[Crossref]

N. V. Tabiryan, S. V. Serak, S. R. Nersisyan, D. E. Roberts, B. Y. Zeldovich, D. M. Steeves, and B. R. Kimball, “Broadband waveplate lenses,” Opt. Express 24(7), 7091–7102 (2016).
[Crossref] [PubMed]

Y. Ke, Z. Liu, Y. Liu, J. Zhou, W. Shu, H. Luo, and S. Wen, “Compact photonic spin filters,” Appl. Phys. Lett. 109(18), 181104 (2016).
[Crossref]

M. J. Tang, P. Chen, W. L. Zhang, A. M. Tam, V. G. Chigrinov, W. Hu, and Y. Q. Lu, “Integrated and reconfigurable optical paths based on stacking optical functional films,” Opt. Express 24(22), 25510–25514 (2016).
[Crossref] [PubMed]

2015 (3)

P. Chen, B. Y. Wei, W. Ji, S. J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y. Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133–139 (2015).
[Crossref]

H. S. Chen, Y. J. Wang, P. J. Chen, and Y. H. Lin, “Electrically adjustable location of a projected image in augmented reality via a liquid-crystal lens,” Opt. Express 23(22), 28154–28162 (2015).
[Crossref] [PubMed]

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

2014 (2)

X. Q. Wang, F. Fan, T. Du, A. M. W. Tam, Y. Ma, A. K. Srivastava, V. G. Chigrinov, and H. S. Kwok, “Liquid crystal Fresnel zone lens based on single-side-patterned photoalignment layer,” Appl. Opt. 53(10), 2026–2029 (2014).
[Crossref] [PubMed]

B. Y. Wei, W. Hu, Y. Ming, F. Xu, S. Rubin, J. G. Wang, V. Chigrinov, and Y. Q. Lu, “Generating switchable and reconfigurable optical vortices via photopatterning of liquid crystals,” Adv. Mater. 26(10), 1590–1595 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (2)

H. Wu, W. Hu, H. C. Hu, X. W. Lin, G. Zhu, J. W. Choi, V. Chigrinov, and Y. Q. Lu, “Arbitrary photo-patterning in liquid crystal alignments using DMD based lithography system,” Opt. Express 20(15), 16684–16689 (2012).
[Crossref]

L. Tan, J. Y. Ho, and H. S. Kwok, “Extended Jones matrix method for oblique incidence study of polarization gratings,” Appl. Phys. Lett. 101(5), 051107 (2012).
[Crossref]

2011 (3)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Y. Li and S. T. Wu, “Polarization independent adaptive microlens with a blue-phase liquid crystal,” Opt. Express 19(9), 8045–8050 (2011).
[Crossref] [PubMed]

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

2009 (1)

2004 (1)

V. Chigrinov, S. Pikin, A. Verevochnikov, V. Kozenkov, M. Khazimullin, J. Ho, D. D. Huang, and H. S. Kwok, “Diffusion model of photoaligning in azo-dye layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(6), 061713 (2004).
[Crossref] [PubMed]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

1987 (1)

M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34(11), 1401–1407 (1987).
[Crossref]

1979 (1)

S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979).
[Crossref]

1952 (1)

S. Pancharatnam, “Generalized theory of interference, and its applications. Part I. Coherent pencils,” Proc. Indian Acad. Sci. A 44, 247–262 (1952).

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Berry, M. V.

M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34(11), 1401–1407 (1987).
[Crossref]

Bowman, R.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

Cai, X. D.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

Chen, H. S.

Chen, M. C.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

Chen, P.

Chen, P. J.

Chigrinov, V.

A. M. Tam, F. Fan, T. Du, W. Hu, W. L. Zhang, C. X. Zhao, X. Q. Wang, K. L. Ching, G. J. Li, H. L. Luo, V. Chigrinov, S. C. Wen, and H. S. Kwok, “Bifocal optical-vortex lens with sorting of the generated nonseparable spin-orbital angular-momentum states,” Phys. Rev. Appl. 7(3), 0304010 (2017).
[Crossref]

P. Chen, B. Y. Wei, W. Ji, S. J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y. Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133–139 (2015).
[Crossref]

B. Y. Wei, W. Hu, Y. Ming, F. Xu, S. Rubin, J. G. Wang, V. Chigrinov, and Y. Q. Lu, “Generating switchable and reconfigurable optical vortices via photopatterning of liquid crystals,” Adv. Mater. 26(10), 1590–1595 (2014).
[Crossref] [PubMed]

H. Wu, W. Hu, H. C. Hu, X. W. Lin, G. Zhu, J. W. Choi, V. Chigrinov, and Y. Q. Lu, “Arbitrary photo-patterning in liquid crystal alignments using DMD based lithography system,” Opt. Express 20(15), 16684–16689 (2012).
[Crossref]

V. Chigrinov, S. Pikin, A. Verevochnikov, V. Kozenkov, M. Khazimullin, J. Ho, D. D. Huang, and H. S. Kwok, “Diffusion model of photoaligning in azo-dye layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(6), 061713 (2004).
[Crossref] [PubMed]

Chigrinov, V. G.

Ching, K. L.

A. M. Tam, F. Fan, T. Du, W. Hu, W. L. Zhang, C. X. Zhao, X. Q. Wang, K. L. Ching, G. J. Li, H. L. Luo, V. Chigrinov, S. C. Wen, and H. S. Kwok, “Bifocal optical-vortex lens with sorting of the generated nonseparable spin-orbital angular-momentum states,” Phys. Rev. Appl. 7(3), 0304010 (2017).
[Crossref]

Choi, J. W.

Denisenko, V.

Desyatnikov, A. S.

Du, T.

A. M. Tam, F. Fan, T. Du, W. Hu, W. L. Zhang, C. X. Zhao, X. Q. Wang, K. L. Ching, G. J. Li, H. L. Luo, V. Chigrinov, S. C. Wen, and H. S. Kwok, “Bifocal optical-vortex lens with sorting of the generated nonseparable spin-orbital angular-momentum states,” Phys. Rev. Appl. 7(3), 0304010 (2017).
[Crossref]

A. M. Tam, F. Fan, H. S. Chen, T. Du, V. G. Chigrinov, Y. H. Lin, and H. S. Kwok, “Nanoscopic patterned photo-alignment for electrically switchable liquid crystal Pancharatnam-Berry phase diffractive lens,” J. Soc. Inf. Disp. 47, 599–601 (2016).

X. Q. Wang, F. Fan, T. Du, A. M. W. Tam, Y. Ma, A. K. Srivastava, V. G. Chigrinov, and H. S. Kwok, “Liquid crystal Fresnel zone lens based on single-side-patterned photoalignment layer,” Appl. Opt. 53(10), 2026–2029 (2014).
[Crossref] [PubMed]

Duan, W.

Fan, F.

A. M. Tam, F. Fan, T. Du, W. Hu, W. L. Zhang, C. X. Zhao, X. Q. Wang, K. L. Ching, G. J. Li, H. L. Luo, V. Chigrinov, S. C. Wen, and H. S. Kwok, “Bifocal optical-vortex lens with sorting of the generated nonseparable spin-orbital angular-momentum states,” Phys. Rev. Appl. 7(3), 0304010 (2017).
[Crossref]

A. M. Tam, F. Fan, H. S. Chen, T. Du, V. G. Chigrinov, Y. H. Lin, and H. S. Kwok, “Nanoscopic patterned photo-alignment for electrically switchable liquid crystal Pancharatnam-Berry phase diffractive lens,” J. Soc. Inf. Disp. 47, 599–601 (2016).

X. Q. Wang, F. Fan, T. Du, A. M. W. Tam, Y. Ma, A. K. Srivastava, V. G. Chigrinov, and H. S. Kwok, “Liquid crystal Fresnel zone lens based on single-side-patterned photoalignment layer,” Appl. Opt. 53(10), 2026–2029 (2014).
[Crossref] [PubMed]

Ge, S. J.

W. Duan, P. Chen, B. Y. Wei, S. J. Ge, X. Liang, W. Hu, and Y. Q. Lu, “Fast-response and high-efficiency optical switch based on dual-frequency liquid crystal polarization grating,” Opt. Mater. Express 6(2), 597–602 (2016).
[Crossref]

P. Chen, B. Y. Wei, W. Ji, S. J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y. Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133–139 (2015).
[Crossref]

Ho, J.

V. Chigrinov, S. Pikin, A. Verevochnikov, V. Kozenkov, M. Khazimullin, J. Ho, D. D. Huang, and H. S. Kwok, “Diffusion model of photoaligning in azo-dye layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(6), 061713 (2004).
[Crossref] [PubMed]

Ho, J. Y.

L. Tan, J. Y. Ho, and H. S. Kwok, “Extended Jones matrix method for oblique incidence study of polarization gratings,” Appl. Phys. Lett. 101(5), 051107 (2012).
[Crossref]

Hu, H. C.

Hu, W.

A. M. Tam, F. Fan, T. Du, W. Hu, W. L. Zhang, C. X. Zhao, X. Q. Wang, K. L. Ching, G. J. Li, H. L. Luo, V. Chigrinov, S. C. Wen, and H. S. Kwok, “Bifocal optical-vortex lens with sorting of the generated nonseparable spin-orbital angular-momentum states,” Phys. Rev. Appl. 7(3), 0304010 (2017).
[Crossref]

W. Duan, P. Chen, B. Y. Wei, S. J. Ge, X. Liang, W. Hu, and Y. Q. Lu, “Fast-response and high-efficiency optical switch based on dual-frequency liquid crystal polarization grating,” Opt. Mater. Express 6(2), 597–602 (2016).
[Crossref]

M. J. Tang, P. Chen, W. L. Zhang, A. M. Tam, V. G. Chigrinov, W. Hu, and Y. Q. Lu, “Integrated and reconfigurable optical paths based on stacking optical functional films,” Opt. Express 24(22), 25510–25514 (2016).
[Crossref] [PubMed]

P. Chen, B. Y. Wei, W. Ji, S. J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y. Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133–139 (2015).
[Crossref]

B. Y. Wei, W. Hu, Y. Ming, F. Xu, S. Rubin, J. G. Wang, V. Chigrinov, and Y. Q. Lu, “Generating switchable and reconfigurable optical vortices via photopatterning of liquid crystals,” Adv. Mater. 26(10), 1590–1595 (2014).
[Crossref] [PubMed]

H. Wu, W. Hu, H. C. Hu, X. W. Lin, G. Zhu, J. W. Choi, V. Chigrinov, and Y. Q. Lu, “Arbitrary photo-patterning in liquid crystal alignments using DMD based lithography system,” Opt. Express 20(15), 16684–16689 (2012).
[Crossref]

Huang, D. D.

V. Chigrinov, S. Pikin, A. Verevochnikov, V. Kozenkov, M. Khazimullin, J. Ho, D. D. Huang, and H. S. Kwok, “Diffusion model of photoaligning in azo-dye layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(6), 061713 (2004).
[Crossref] [PubMed]

Ji, W.

P. Chen, B. Y. Wei, W. Ji, S. J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y. Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133–139 (2015).
[Crossref]

Ke, Y.

Y. Ke, Z. Liu, Y. Liu, J. Zhou, W. Shu, H. Luo, and S. Wen, “Compact photonic spin filters,” Appl. Phys. Lett. 109(18), 181104 (2016).
[Crossref]

Khazimullin, M.

V. Chigrinov, S. Pikin, A. Verevochnikov, V. Kozenkov, M. Khazimullin, J. Ho, D. D. Huang, and H. S. Kwok, “Diffusion model of photoaligning in azo-dye layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(6), 061713 (2004).
[Crossref] [PubMed]

Kimball, B. R.

Kivshar, Y. S.

Kozenkov, V.

V. Chigrinov, S. Pikin, A. Verevochnikov, V. Kozenkov, M. Khazimullin, J. Ho, D. D. Huang, and H. S. Kwok, “Diffusion model of photoaligning in azo-dye layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(6), 061713 (2004).
[Crossref] [PubMed]

Krolikowski, W.

Kwok, H. S.

A. M. Tam, F. Fan, T. Du, W. Hu, W. L. Zhang, C. X. Zhao, X. Q. Wang, K. L. Ching, G. J. Li, H. L. Luo, V. Chigrinov, S. C. Wen, and H. S. Kwok, “Bifocal optical-vortex lens with sorting of the generated nonseparable spin-orbital angular-momentum states,” Phys. Rev. Appl. 7(3), 0304010 (2017).
[Crossref]

A. M. Tam, F. Fan, H. S. Chen, T. Du, V. G. Chigrinov, Y. H. Lin, and H. S. Kwok, “Nanoscopic patterned photo-alignment for electrically switchable liquid crystal Pancharatnam-Berry phase diffractive lens,” J. Soc. Inf. Disp. 47, 599–601 (2016).

X. Q. Wang, F. Fan, T. Du, A. M. W. Tam, Y. Ma, A. K. Srivastava, V. G. Chigrinov, and H. S. Kwok, “Liquid crystal Fresnel zone lens based on single-side-patterned photoalignment layer,” Appl. Opt. 53(10), 2026–2029 (2014).
[Crossref] [PubMed]

L. Tan, J. Y. Ho, and H. S. Kwok, “Extended Jones matrix method for oblique incidence study of polarization gratings,” Appl. Phys. Lett. 101(5), 051107 (2012).
[Crossref]

V. Chigrinov, S. Pikin, A. Verevochnikov, V. Kozenkov, M. Khazimullin, J. Ho, D. D. Huang, and H. S. Kwok, “Diffusion model of photoaligning in azo-dye layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(6), 061713 (2004).
[Crossref] [PubMed]

Li, G. J.

A. M. Tam, F. Fan, T. Du, W. Hu, W. L. Zhang, C. X. Zhao, X. Q. Wang, K. L. Ching, G. J. Li, H. L. Luo, V. Chigrinov, S. C. Wen, and H. S. Kwok, “Bifocal optical-vortex lens with sorting of the generated nonseparable spin-orbital angular-momentum states,” Phys. Rev. Appl. 7(3), 0304010 (2017).
[Crossref]

Li, L.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

Li, Y.

Liang, X.

Lin, X. W.

Lin, Y. H.

Liu, N. L.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

Liu, Y.

Y. Ke, Z. Liu, Y. Liu, J. Zhou, W. Shu, H. Luo, and S. Wen, “Compact photonic spin filters,” Appl. Phys. Lett. 109(18), 181104 (2016).
[Crossref]

Liu, Z.

Y. Ke, Z. Liu, Y. Liu, J. Zhou, W. Shu, H. Luo, and S. Wen, “Compact photonic spin filters,” Appl. Phys. Lett. 109(18), 181104 (2016).
[Crossref]

Lu, C. Y.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

Lu, Y. Q.

Luo, H.

Y. Ke, Z. Liu, Y. Liu, J. Zhou, W. Shu, H. Luo, and S. Wen, “Compact photonic spin filters,” Appl. Phys. Lett. 109(18), 181104 (2016).
[Crossref]

Luo, H. L.

A. M. Tam, F. Fan, T. Du, W. Hu, W. L. Zhang, C. X. Zhao, X. Q. Wang, K. L. Ching, G. J. Li, H. L. Luo, V. Chigrinov, S. C. Wen, and H. S. Kwok, “Bifocal optical-vortex lens with sorting of the generated nonseparable spin-orbital angular-momentum states,” Phys. Rev. Appl. 7(3), 0304010 (2017).
[Crossref]

Ma, Y.

Ming, Y.

B. Y. Wei, W. Hu, Y. Ming, F. Xu, S. Rubin, J. G. Wang, V. Chigrinov, and Y. Q. Lu, “Generating switchable and reconfigurable optical vortices via photopatterning of liquid crystals,” Adv. Mater. 26(10), 1590–1595 (2014).
[Crossref] [PubMed]

Nersisyan, S. R.

Neshev, D. N.

Padgett, M.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

Padgett, M. J.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Pan, J. W.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

Pancharatnam, S.

S. Pancharatnam, “Generalized theory of interference, and its applications. Part I. Coherent pencils,” Proc. Indian Acad. Sci. A 44, 247–262 (1952).

Pikin, S.

V. Chigrinov, S. Pikin, A. Verevochnikov, V. Kozenkov, M. Khazimullin, J. Ho, D. D. Huang, and H. S. Kwok, “Diffusion model of photoaligning in azo-dye layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(6), 061713 (2004).
[Crossref] [PubMed]

Roberts, D. E.

Rubin, S.

B. Y. Wei, W. Hu, Y. Ming, F. Xu, S. Rubin, J. G. Wang, V. Chigrinov, and Y. Q. Lu, “Generating switchable and reconfigurable optical vortices via photopatterning of liquid crystals,” Adv. Mater. 26(10), 1590–1595 (2014).
[Crossref] [PubMed]

Sato, S.

S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979).
[Crossref]

Serak, S. V.

Shu, W.

Y. Ke, Z. Liu, Y. Liu, J. Zhou, W. Shu, H. Luo, and S. Wen, “Compact photonic spin filters,” Appl. Phys. Lett. 109(18), 181104 (2016).
[Crossref]

Shvedov, V.

Soskin, M.

Spreeuw, R. J.

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Srivastava, A. K.

Steeves, D. M.

Su, Z. E.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

Tabiryan, N. V.

Tam, A. M.

A. M. Tam, F. Fan, T. Du, W. Hu, W. L. Zhang, C. X. Zhao, X. Q. Wang, K. L. Ching, G. J. Li, H. L. Luo, V. Chigrinov, S. C. Wen, and H. S. Kwok, “Bifocal optical-vortex lens with sorting of the generated nonseparable spin-orbital angular-momentum states,” Phys. Rev. Appl. 7(3), 0304010 (2017).
[Crossref]

A. M. Tam, F. Fan, H. S. Chen, T. Du, V. G. Chigrinov, Y. H. Lin, and H. S. Kwok, “Nanoscopic patterned photo-alignment for electrically switchable liquid crystal Pancharatnam-Berry phase diffractive lens,” J. Soc. Inf. Disp. 47, 599–601 (2016).

M. J. Tang, P. Chen, W. L. Zhang, A. M. Tam, V. G. Chigrinov, W. Hu, and Y. Q. Lu, “Integrated and reconfigurable optical paths based on stacking optical functional films,” Opt. Express 24(22), 25510–25514 (2016).
[Crossref] [PubMed]

Tam, A. M. W.

Tan, L.

L. Tan, J. Y. Ho, and H. S. Kwok, “Extended Jones matrix method for oblique incidence study of polarization gratings,” Appl. Phys. Lett. 101(5), 051107 (2012).
[Crossref]

Tang, M. J.

Verevochnikov, A.

V. Chigrinov, S. Pikin, A. Verevochnikov, V. Kozenkov, M. Khazimullin, J. Ho, D. D. Huang, and H. S. Kwok, “Diffusion model of photoaligning in azo-dye layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(6), 061713 (2004).
[Crossref] [PubMed]

Volyar, A.

Wang, J.

J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4(5), B14–B28 (2016).
[Crossref]

Wang, J. G.

B. Y. Wei, W. Hu, Y. Ming, F. Xu, S. Rubin, J. G. Wang, V. Chigrinov, and Y. Q. Lu, “Generating switchable and reconfigurable optical vortices via photopatterning of liquid crystals,” Adv. Mater. 26(10), 1590–1595 (2014).
[Crossref] [PubMed]

Wang, X. L.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

Wang, X. Q.

A. M. Tam, F. Fan, T. Du, W. Hu, W. L. Zhang, C. X. Zhao, X. Q. Wang, K. L. Ching, G. J. Li, H. L. Luo, V. Chigrinov, S. C. Wen, and H. S. Kwok, “Bifocal optical-vortex lens with sorting of the generated nonseparable spin-orbital angular-momentum states,” Phys. Rev. Appl. 7(3), 0304010 (2017).
[Crossref]

X. Q. Wang, F. Fan, T. Du, A. M. W. Tam, Y. Ma, A. K. Srivastava, V. G. Chigrinov, and H. S. Kwok, “Liquid crystal Fresnel zone lens based on single-side-patterned photoalignment layer,” Appl. Opt. 53(10), 2026–2029 (2014).
[Crossref] [PubMed]

Wang, Y. J.

Wei, B. Y.

W. Duan, P. Chen, B. Y. Wei, S. J. Ge, X. Liang, W. Hu, and Y. Q. Lu, “Fast-response and high-efficiency optical switch based on dual-frequency liquid crystal polarization grating,” Opt. Mater. Express 6(2), 597–602 (2016).
[Crossref]

P. Chen, B. Y. Wei, W. Ji, S. J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y. Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133–139 (2015).
[Crossref]

B. Y. Wei, W. Hu, Y. Ming, F. Xu, S. Rubin, J. G. Wang, V. Chigrinov, and Y. Q. Lu, “Generating switchable and reconfigurable optical vortices via photopatterning of liquid crystals,” Adv. Mater. 26(10), 1590–1595 (2014).
[Crossref] [PubMed]

Wen, S.

Y. Ke, Z. Liu, Y. Liu, J. Zhou, W. Shu, H. Luo, and S. Wen, “Compact photonic spin filters,” Appl. Phys. Lett. 109(18), 181104 (2016).
[Crossref]

Wen, S. C.

A. M. Tam, F. Fan, T. Du, W. Hu, W. L. Zhang, C. X. Zhao, X. Q. Wang, K. L. Ching, G. J. Li, H. L. Luo, V. Chigrinov, S. C. Wen, and H. S. Kwok, “Bifocal optical-vortex lens with sorting of the generated nonseparable spin-orbital angular-momentum states,” Phys. Rev. Appl. 7(3), 0304010 (2017).
[Crossref]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Wu, D.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

Wu, H.

Wu, S. T.

Xu, F.

P. Chen, B. Y. Wei, W. Ji, S. J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y. Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133–139 (2015).
[Crossref]

B. Y. Wei, W. Hu, Y. Ming, F. Xu, S. Rubin, J. G. Wang, V. Chigrinov, and Y. Q. Lu, “Generating switchable and reconfigurable optical vortices via photopatterning of liquid crystals,” Adv. Mater. 26(10), 1590–1595 (2014).
[Crossref] [PubMed]

Yao, A. M.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Zeldovich, B. Y.

Zhang, W. L.

A. M. Tam, F. Fan, T. Du, W. Hu, W. L. Zhang, C. X. Zhao, X. Q. Wang, K. L. Ching, G. J. Li, H. L. Luo, V. Chigrinov, S. C. Wen, and H. S. Kwok, “Bifocal optical-vortex lens with sorting of the generated nonseparable spin-orbital angular-momentum states,” Phys. Rev. Appl. 7(3), 0304010 (2017).
[Crossref]

M. J. Tang, P. Chen, W. L. Zhang, A. M. Tam, V. G. Chigrinov, W. Hu, and Y. Q. Lu, “Integrated and reconfigurable optical paths based on stacking optical functional films,” Opt. Express 24(22), 25510–25514 (2016).
[Crossref] [PubMed]

Zhao, C. X.

A. M. Tam, F. Fan, T. Du, W. Hu, W. L. Zhang, C. X. Zhao, X. Q. Wang, K. L. Ching, G. J. Li, H. L. Luo, V. Chigrinov, S. C. Wen, and H. S. Kwok, “Bifocal optical-vortex lens with sorting of the generated nonseparable spin-orbital angular-momentum states,” Phys. Rev. Appl. 7(3), 0304010 (2017).
[Crossref]

Zhou, J.

Y. Ke, Z. Liu, Y. Liu, J. Zhou, W. Shu, H. Luo, and S. Wen, “Compact photonic spin filters,” Appl. Phys. Lett. 109(18), 181104 (2016).
[Crossref]

Zhu, G.

Adv. Mater. (1)

B. Y. Wei, W. Hu, Y. Ming, F. Xu, S. Rubin, J. G. Wang, V. Chigrinov, and Y. Q. Lu, “Generating switchable and reconfigurable optical vortices via photopatterning of liquid crystals,” Adv. Mater. 26(10), 1590–1595 (2014).
[Crossref] [PubMed]

Adv. Opt. Photonics (1)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

Y. Ke, Z. Liu, Y. Liu, J. Zhou, W. Shu, H. Luo, and S. Wen, “Compact photonic spin filters,” Appl. Phys. Lett. 109(18), 181104 (2016).
[Crossref]

L. Tan, J. Y. Ho, and H. S. Kwok, “Extended Jones matrix method for oblique incidence study of polarization gratings,” Appl. Phys. Lett. 101(5), 051107 (2012).
[Crossref]

J. Mod. Opt. (1)

M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34(11), 1401–1407 (1987).
[Crossref]

J. Soc. Inf. Disp. (1)

A. M. Tam, F. Fan, H. S. Chen, T. Du, V. G. Chigrinov, Y. H. Lin, and H. S. Kwok, “Nanoscopic patterned photo-alignment for electrically switchable liquid crystal Pancharatnam-Berry phase diffractive lens,” J. Soc. Inf. Disp. 47, 599–601 (2016).

Jpn. J. Appl. Phys. (1)

S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979).
[Crossref]

Nat. Photonics (1)

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

Nature (1)

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

Opt. Express (7)

V. Denisenko, V. Shvedov, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, A. Volyar, M. Soskin, and Y. S. Kivshar, “Determination of topological charges of polychromatic optical vortices,” Opt. Express 17(26), 23374–23379 (2009).
[Crossref] [PubMed]

Y. Li and S. T. Wu, “Polarization independent adaptive microlens with a blue-phase liquid crystal,” Opt. Express 19(9), 8045–8050 (2011).
[Crossref] [PubMed]

H. Wu, W. Hu, H. C. Hu, X. W. Lin, G. Zhu, J. W. Choi, V. Chigrinov, and Y. Q. Lu, “Arbitrary photo-patterning in liquid crystal alignments using DMD based lithography system,” Opt. Express 20(15), 16684–16689 (2012).
[Crossref]

Y. H. Lin and H. S. Chen, “Electrically tunable-focusing and polarizer-free liquid crystal lenses for ophthalmic applications,” Opt. Express 21(8), 9428–9436 (2013).
[Crossref] [PubMed]

H. S. Chen, Y. J. Wang, P. J. Chen, and Y. H. Lin, “Electrically adjustable location of a projected image in augmented reality via a liquid-crystal lens,” Opt. Express 23(22), 28154–28162 (2015).
[Crossref] [PubMed]

N. V. Tabiryan, S. V. Serak, S. R. Nersisyan, D. E. Roberts, B. Y. Zeldovich, D. M. Steeves, and B. R. Kimball, “Broadband waveplate lenses,” Opt. Express 24(7), 7091–7102 (2016).
[Crossref] [PubMed]

M. J. Tang, P. Chen, W. L. Zhang, A. M. Tam, V. G. Chigrinov, W. Hu, and Y. Q. Lu, “Integrated and reconfigurable optical paths based on stacking optical functional films,” Opt. Express 24(22), 25510–25514 (2016).
[Crossref] [PubMed]

Opt. Mater. Express (1)

Photonics Res. (2)

P. Chen, B. Y. Wei, W. Ji, S. J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y. Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133–139 (2015).
[Crossref]

J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4(5), B14–B28 (2016).
[Crossref]

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Phys. Rev. Appl. (1)

A. M. Tam, F. Fan, T. Du, W. Hu, W. L. Zhang, C. X. Zhao, X. Q. Wang, K. L. Ching, G. J. Li, H. L. Luo, V. Chigrinov, S. C. Wen, and H. S. Kwok, “Bifocal optical-vortex lens with sorting of the generated nonseparable spin-orbital angular-momentum states,” Phys. Rev. Appl. 7(3), 0304010 (2017).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

V. Chigrinov, S. Pikin, A. Verevochnikov, V. Kozenkov, M. Khazimullin, J. Ho, D. D. Huang, and H. S. Kwok, “Diffusion model of photoaligning in azo-dye layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(6), 061713 (2004).
[Crossref] [PubMed]

Proc. Indian Acad. Sci. A (1)

S. Pancharatnam, “Generalized theory of interference, and its applications. Part I. Coherent pencils,” Proc. Indian Acad. Sci. A 44, 247–262 (1952).

Other (1)

H. Ren and S. T. Wu, Introduction to Adaptive Lenses (John Wiley, 2012).

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Figures (4)

Fig. 1
Fig. 1 The theoretical director distributions (a)-(c) and corresponding micrographs (d)-(f) of PFVLs with m = 1, m = 2 and m = 8, respectively. The scale bar is 200 μm.
Fig. 2
Fig. 2 Scheme of the optical setup for generating and detecting (de-)focused vortices.
Fig. 3
Fig. 3 The intensity images of generated focused/defocused vortex beams corresponding to (a) RCP, (b) LCP and (c) linearly polarized incident beams. (d)-(f) show the images corresponding to the horizontally flipped samples.
Fig. 4
Fig. 4 The astigmatic transformation of optical vortices with (a) m = 1, (b) m = 2 and (c) m = 8.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

α= πx /Λ + 1 2 mφ+ π λ ( r 2 + f 2 f ),
T = R(α)[ exp(iΓ/2) 0 0 exp(iΓ/2) ]R(α) =cos Γ 2 Iisin Γ 2 [ cos2α sin2α sin2α cos2α ],
E out =T E in =cos Γ 2 χ (±) isin Γ 2 exp[ ±imφi2 πx /Λ ±i 2π λ ( r 2 + f 2 f ) ] χ () .

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